Much is known about the molecular components involved in signal transduction and gene expression in a number of systems, and the focus is now shifting to understanding how these components are integrated into networks, and how these networks transduce the inputs they receive and produce the desired pattern of gene expression in a developing system. Development is a sequential process in which later stages build on earlier stages, but within stages there are often multiple feedback loops in signaling and gene control networks that may serve to buffer against perturbations caused by fluctuations in signaling molecules and other components. One of the long range objectives of this research are to develop mathematical and computational tools that can be used to shed light on the structural characteristics of networks that lead to reliable outputs in the face of parametric, environmental and molecular fluctuations. Drosophila melanogaster is one of several model systems for which many of the components of the signal transduction and gene control networks involved in patterning are known. However, less is known about how these networks produce the desired spatio-temporal pattern of gene expression. The major projects are: (1) studies on dorsal-ventral patterning in Drosophila, (2) studies on growth and patterning in the wing disc of Drosophila, an (3) studies on dorsal-ventral patterning in the African frog Drosophila, Xenopus laevis. The aims under (1) are to further advance our understanding of the role of stochastic fluctuations and the role of certain mutants, and to begin a study of the role of non-receptor (auxiliary) proteins in modulating signaling. We will develop a general model for this and analyze how the balance between different factors such as collagen and surface bound proteins affect characteristics such as noise in gene expression and robustness in the face of mutations and other perturbations. The aims under (2) are to develop and analyze a hierarchy of models for pattern formation and growth in the Drosophila wing disc to understand how distinct signaling pathways interact in a geometrically- realistic representation of a disc. The objectives under (3) are to understand BMP signaling and patterning in Xenopus and to identify the source of size-adaptation in the development of Xenopus. PUBLIC HEALTH RELEVANCE: The research will advance our understanding of basic processes in developmental biology such as signal transduction, pattern formation and the control of organ size in developing systems. A better understanding of these fundamental processes will contribute to a better understanding of how systems respond to their environment, how normal development can be disrupted and perhaps abnormal development corrected. In particular, understanding growth control in normal systems will be essential for understanding aberrant control in cancer.